Aither is a double-blind peer review, Open Access online academic journal. It is indexed at ERIH+ and Scopus. It is published by the Faculty of Arts of the Palacký University in Olomouc in cooperation with the Philosophical Institute of the Academy of Sciences of the Czech Republic. It comes out twice a year. Every second issue is international and contains foreign-language articles (mainly in English, but also in German and French). The journal is registered under the number ISSN 1803-7860.

Aither 23/2020 (International issue no. 7):58-85 | DOI: 10.5507/aither.2020.005

The Renaissance of Numbers: on Continuity, Nature of Complex Numbers and the Symbolic Turn

Jan Makovský
Center for Theoretical Study, Charles University & Czech Academy of Sciences

The paper presents an analysis of imaginary quantity before Gauss based on the notion of continuity and symbolic representation. Its aim is to uncover subtle roots of the "impossible", "sophisticated" or "absurd" entities that, as we claim, stem from the Renaissance notion of nature and from the "symbolic turn" which occurred in that period. In order to grant impossible quantities a reasonable (operational) meaning, it is necessary to establish an equation (formal continuity) between real and imaginary. It is possible only if the real is in a sense subsumed within the symbolic which holds paradigmatically for the notions of number and magnitude. For, once number and magnitude become symbolic representations of the same universal intellectual matter of quantity, an operational analogy and continuity between them may be established. Three "continuities" shall be distinguished on the path to such "universal mathematics" at the end of which the imaginary entities may acquire the citizenship in the Republic of numbers.

Published: March 30, 2020  Show citation

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Makovský, J. (2020). The Renaissance of Numbers: on Continuity, Nature of Complex Numbers and the Symbolic Turn. Aither, 12(23), 58-85. doi: 10.5507/aither.2020.005
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